Solving the heat equation symbolically with MuSimp
We derive an algorithm suitable for a small computer algebra system (MuSimp) which solves the heat equation given inital values \(u(x,t_ 0)=\phi (x)\), where \(\phi\) is a polynomial, without having to evaluate the heat integral. Uniqueness of the solutions follows from the fact that polynomial solutions of the heat equation have Huygens' property. We also derive an algorithm for the boundary value (finite bar) problem. We first discuss the case of one space dimension.
scientific article; zbMATH DE number 4097899